%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC385+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:03:44 PM UTC 2026
% Result : Theorem 2.60s 1.07s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 12 unt; 3 def)
% Number of atoms : 92 ( 12 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 96 ( 31 ~; 23 |; 31 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ~ segmentP(X3,X2)
| ( ~ singletonP(X2)
& neq(X3,nil) )
| ( singletonP(X0)
& segmentP(X1,X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ~ segmentP(X3,X2)
| ( ~ singletonP(X2)
& neq(X3,nil) )
| ( singletonP(X0)
& segmentP(X1,X0) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& segmentP(X3,X2)
& ( singletonP(X2)
| ~ neq(X3,nil) )
& ( ~ singletonP(X0)
| ~ segmentP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& segmentP(X3,X2)
& ( singletonP(X2)
| ~ neq(X3,nil) )
& ( ~ singletonP(X0)
| ~ segmentP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f113,plain,
( sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& segmentP(sK3,sK2)
& ( singletonP(sK2)
| ~ neq(sK3,nil) )
& ( ~ singletonP(sK0)
| ~ segmentP(sK1,sK0) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f127,plain,
( ~ singletonP(sK0)
| ~ segmentP(sK1,sK0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f128,plain,
( singletonP(sK2)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f113]) ).
fof(f129,plain,
segmentP(sK3,sK2),
inference(cnf_transformation,[],[f113]) ).
fof(f130,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f113]) ).
fof(f131,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f113]) ).
fof(f132,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f113]) ).
fof(f153,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f130,f132]) ).
fof(f154,plain,
( ~ singletonP(sK2)
| ~ segmentP(sK3,sK2) ),
inference(definition_unfolding,[],[f127,f131,f132,f131]) ).
fof(f166,definition,
( spl8_1
<=> segmentP(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f170,definition,
( spl8_2
<=> singletonP(sK2) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f173,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f154,f170,f166]) ).
fof(f175,definition,
( spl8_3
<=> neq(sK3,nil) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f178,plain,
( ~ spl8_3
| spl8_2 ),
inference(avatar_split_clause,[],[f128,f170,f175]) ).
fof(f179,plain,
spl8_1,
inference(avatar_split_clause,[],[f129,f166]) ).
fof(f180,plain,
spl8_3,
inference(avatar_split_clause,[],[f153,f175]) ).
cnf(s1,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f173]) ).
cnf(s2,plain,
( spl8_2
| ~ spl8_3 ),
inference(sat_conversion,[],[f178]) ).
cnf(s3,plain,
spl8_1,
inference(sat_conversion,[],[f179]) ).
cnf(s4,plain,
spl8_3,
inference(sat_conversion,[],[f180]) ).
cnf(s5,plain,
spl8_2,
inference(rat,[],[s2,s4]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s3]) ).
fof(f181,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC385+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 09:21:25 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/1.07 % (2263991)Detected formulas, will run a generic FOF schedule.
% 2.60/1.07 % (2263999)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=45664951:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.07 % (2263999)First to succeed.
% 2.60/1.07 % (2263999)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2263991"
% 2.60/1.07 % (2264001)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=542103300:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.07 % (2263996)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=784415312:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.07 % (2263998)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1759483560:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.07 % (2263997)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3988015131:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.07 % (2264001)Also succeeded, but the first one will report.
% 2.60/1.07 % (2264000)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=497133633:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.07 % (2264002)dis-21_1_sil=8000:lcm=predicate:random_seed=1189294667:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.60/1.07 % (2264000)Also succeeded, but the first one will report.
% 2.60/1.07 % (2264002)Also succeeded, but the first one will report.
% 2.60/1.07 % (2263999)Refutation found. Thanks to Tanya!
% 2.60/1.07 % SZS status Theorem for theBenchmark
% 2.60/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.07 % (2263999)------------------------------
% 2.60/1.07 % (2263999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.07 % (2263999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.07 % (2263999)CaDiCaL version: 2.1.3
% 2.60/1.07 % (2263999)Termination reason: Refutation
% 2.60/1.07 % (2263999)Time elapsed: 0.002 s
% 2.60/1.07 % (2263999)Peak memory usage: 89 MB
% 2.60/1.07 % (2263999)Instructions burned: 2 (million)
% 2.60/1.07 % (2263999)------------------------------
% 2.60/1.07 % (2263999)------------------------------
% 2.60/1.07 % (2263991)Success in time 0.287 s
% 2.60/1.07 % Vampire exiting
%------------------------------------------------------------------------------